Year: 2025
Author: Fang Chen, Meng Li, Yanmin Zhao
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 641–672
Abstract
This paper presents three regularized models for the logarithmic Klein-Gordon equation. By using a modified Crank-Nicolson method in time and the Galerkin finite element method (FEM) in space, a fully implicit energy-conservative numerical scheme is constructed for the local energy regularized model that is regarded as the best one among the three regularized models. Then, the cut-off function technique and the time-space error splitting technique are innovatively combined to rigorously analyze the unconditionally optimal and high-accuracy convergence results of the numerical scheme without any coupling condition between the temporal step size and the spatial mesh width. The theoretical framework is uniform for the other two regularized models. Finally, numerical experiments are provided to verify our theoretical results. The analytical techniques in this work are not limited in the FEM, and can be directly extended into other numerical methods. More importantly, this work closes the gap for the unconditional error/stability analysis of the numerical methods for the logarithmic systems in higher dimensional spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2312-m2023-0185
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 641–672
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Logarithmic Klein-Gordon equation Finite element method Cut-off Error splitting technique Convergence.